1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vitek1552 [10]
3 years ago
12

Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsda

y equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Mathematics
1 answer:
stich3 [128]3 years ago
4 0

Answer:

The doomsday is 146 days

<em></em>

Step-by-step explanation:

Given

\frac{dy}{dt} = ky^{1 +c}

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

\frac{dt}{y^{1+c}}

\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}

\frac{dy}{y^{1+c}}  = k\ dt

Take integral of both sides

\int \frac{dy}{y^{1+c}}  = \int k\ dt

\int y^{-1-c}\ dy  = \int k\ dt

\int y^{-1-c}\ dy  = k\int\ dt

Integrate

\frac{y^{-1-c+1}}{-1-c+1} = kt+C

-\frac{y^{-c}}{c} = kt+C

To find c; let t= 0

-\frac{y_0^{-c}}{c} = k*0+C

-\frac{y_0^{-c}}{c} = C

C =-\frac{y_0^{-c}}{c}

Substitute C =-\frac{y_0^{-c}}{c} in -\frac{y^{-c}}{c} = kt+C

-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}

Multiply through by -c

y^{-c} = -ckt+y_0^{-c}

Take exponents of -c^{-1

y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}

y = [-ckt+y_0^{-c}]^{-c^{-1}

y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}

i.e.

y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}

Next:

t= 3 i.e. 3 months

y_0 = 2 --- initial number of breeds

So, we have:

y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}

-----------------------------------------------------------------------------

We have the growth term to be: ky^{1.01}

This implies that:

ky^{1.01} = ky^{1+c}

By comparison:

1.01 = 1 + c

c = 1.01 - 1 = 0.01

y(3) = 16 --- 16 rabbits after 3 months:

-----------------------------------------------------------------------------

y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}

16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}

16 = [-0.03 * k + 2^{-0.01}]^{-100}

16 = [-0.03 k + 0.9931]^{-100}

Take -1/100th root of both sides

16^{-1/100} = -0.03k + 0.9931

0.9727 = -0.03k + 0.9931

0.03k= - 0.9727 + 0.9931

0.03k= 0.0204

k= \frac{0.0204}{0.03}

k= 0.68

Recall that:

-\frac{y^{-c}}{c} = kt+C

This implies that:

\frac{y_0^{-c}}{c} = kT

Make T the subject

T = \frac{y_0^{-c}}{kc}

Substitute: k= 0.68, c = 0.01 and y_0 = 2

T = \frac{2^{-0.01}}{0.68 * 0.01}

T = \frac{2^{-0.01}}{0.0068}

T = \frac{0.9931}{0.0068}

T = 146.04

<em>The doomsday is 146 days</em>

You might be interested in
3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third
mars1129 [50]

The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

<h3>Inequalities </h3>

From the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle

From the given information,

Line DE is about half the length of line DF

That is,

ED = 1/2 DF

Also,

Line FE is about one-third of the length of line DF

That is,

EF = 1/3 DF

Then, we can write that

ED + EF = 1/2DF + 1/3DF

ED + EF = 5/6 DF

Since,

5/6 DF < DF

Then,

ED + EF < DF

Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

Learn more on Inequalities here: brainly.com/question/1447311

#SPJ1

5 0
2 years ago
Math help please!
Dovator [93]

Answer:

x || t,         [Given]  

m\angle 16 = m\angle 7     [Given]                      ......[1]

Transversal defined as a line that cuts across two or more Parallel lines.

When two parallel lines are cut by a transversal, then the pairs of corresponding angles are equal in measure.

m\angle 16 = m\angle 1   [Corresponding Angle theorem]     ......[2]

Substitute value [1] in [2] we have;

m\angle 7 =m\angle 1   [Substitution Property]

When two lines are cut by a transversal and the alternate exterior angles are equal in measure, then the lines are parallel.

k || w                     [ By Alternative Exterior Angle Theorem]       Hence proved!

3 0
3 years ago
-4(2x+3)-2 <br> Show and explain work <br> (Distributive property)
Alexeev081 [22]

Answer:

The answer is -8x-10

Step-by-step explanation:

-4(2x+3)-2

you will use the -4 to open the bracket

-8x-12-2

-8x-10

5 0
3 years ago
Please help very important!!!! ( dont steal or guess) (I will give brainiest if you have proof)
velikii [3]

Answer:

A) AA

Step-by-step explanation:

We\ are\ given\ that\\\The\ Angles\  of\ \triangle 1,\ are\ 40, 100\\The\ Angles\  of\ \triangle 2\ are\ 40, 40\\The\ Hence,\\Through\ Angle\ Sum\ Property\ Of\ A\ Triangle, \\The\ Angles\  of\ \triangle 1,\ are\ 40, 100,40\\The\ Angles\  of\ \triangle 2\ are\ 40, 40,100\\\\As\ we\ can\ observe\ that\ all\ ANGLES\ of\ the\ triangles\ correspond, \\through\ AA\ Similarity\ Postulate. which\ states\ that\ if\ two\ triangles\ have\ two\\ or\ more\ corresponding\ angles,\ the\ triangles\ are

SIMILAR

4 0
3 years ago
Please help will give brainlyest need help asap
iren2701 [21]

Answer:

friend me on here and imma send you the link Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
    6·1 answer
  • Peter owns a hotel. He has found that when he charges $119 for a night’s stay, the average occupancy is 372 people. In addition,
    7·1 answer
  • Find the midpoint of the segment with the following endpoints. (5,3) and (1,9)
    6·1 answer
  • Solve the equation for the variable r/4=18​
    11·2 answers
  • What is the lcm of 44 36
    6·1 answer
  • 3. Why is it true that finding a square root is the inverse of squaring?
    6·2 answers
  • Under a dilation of a scale factor of 1/2 centered at (7,5), SM becomes HG. Determine the coordinates of HG
    8·1 answer
  • I need help someone please
    7·1 answer
  • A recipe calls for 4/5 cup of milk and 1/2 cup of rice. How much more milk than rice is needed?
    12·2 answers
  • Pls explain and provide calculation thank you
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!